As stated above, we have solved numerically eqs. (REF )-() by using a shooting method finding an excellent agreement with the limiting results presented in the literature. (Note that in the absence of portals, parametrized by \(\xi \) , \(\kappa _3\)  and \(\Phi _g\) , the system becomes two uncoupled copies of a Maxwell-Higgs theory, whose solution is well documented in the literature [1]}, [2]}, [3]}). Since the KM and HP have been extensively studied before (e.g. [4]}, [5]}, [6]}), here we focus on highlighting the behaviour of our model when the SGI portal is present and compare its effect with those of the other two portals.
